NL200 button min 4 bet

[Cashane]

Button is a 23/12/2 regular, seems tight weak with a low wsd% (<25%) and a high %showdowns won(>65%). I play somewhere around 20/16/2, and vilain probably suspects I can 3 bet light.

NL $1/$2 Texas Hold'em
Table 6-max (Real Money)
Seat 3 is the button
Total number of active players : 6
Seat 1: MP ( $171.20 )
Seat 2: CO ( $168.90 )
Seat 3: <font color="blue">Button</font> ( $195 )
Seat 4: <font color="red">Hero</font> ( $305.45 )
Seat 5: BB ( $250.10 )
Seat 6: UTG ( $188.45 )
<font color="red">Hero</font> posts small blind [$1]
BB posts big blind [$2]
** Dealing down cards **
Dealt to <font color="red">Hero</font> K [img]/images/graemlins/spade.gif[/img] K [img]/images/graemlins/heart.gif[/img]
UTG folds
MP folds
CO folds
<font color="blue">Button</font> raises to [$7]
<font color="red">Hero</font> raises to [$28]
BB folds
<font color="blue">Button</font> raises to [$49]
<font color="red">Hero</font> goes all-in
<font color="red">Hero</font> raises to [$305.45]
<font color="blue">Button</font> folds
Returning uncalled bet [$256.45] to Hero
** Hand Conclusion **
<font color="red">Hero</font> wins $100 from main pot

What kind of hands should I expect the most if I just call instead of shoving (mostly QQ/JJ? possibly AQ/AK? Or should I also expect light hands like 89s trying to resteal and to get vigorish + position if I call?).

And also which line is best? Push, call and check flop, call and lead? I chose to push since oop, but I'm not convinced it's the best choice..
I suspect the player plays too solid to call the push with AK or QQ-, or rarely, and I have to take into account the possibility he might also do this min 4 bet with AA.